HeKS said: So even after the reconciliation at the end of LC, they still make it clear that he wants to keep using Indiana and not switch to Henry Jones Jr.
The finale of LC takes place 18 years prior to KotCS...people change. It's clear from Skull that Indy is both:
A. Now comfortable with being Henry Jones, jr. He now uses it as his name in professional circles, ie: at college.
B. Still thinks of himself as Indy first and foremost. His first instinct when meeting Ox is to call himself Indiana.
In my opinion, however, no explanation would be good enough considering the movie is called INDIANA JONES AND THE KINGDOM OF THE CRYSTAL SKULL
And the main character is Indiana Jones. Just because he has another name that he uses, doesn't really change that. No one is saying that he should or does go by Henry, jr. exclusively.
It's no different to Bruce Wayne being the main character in "Batman Begins".
Either way, it's not as though I have an objection to someone "Indy-ing" up the dialogue. :)